2x^2+14x-72=0

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Solution for 2x^2+14x-72=0 equation: 


Simplifying
2x2 + 14x + -72 = 0

Reorder the terms:
-72 + 14x + 2x2 = 0

Solving
-72 + 14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + 7x + x2 = 0

Solving
-36 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 7x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 7x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 7x + x2 = 0 + 36
7x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
7x + x2 = 36

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 36 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 36 + 12.25

Combine like terms: 36 + 12.25 = 48.25
12.25 + 7x + x2 = 48.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x + 3.5 = 6.946221995

Simplifying
x + 3.5 = 6.946221995

Reorder the terms:
3.5 + x = 6.946221995

Solving
3.5 + x = 6.946221995

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 6.946221995 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.946221995 + -3.5
x = 6.946221995 + -3.5

Combine like terms: 6.946221995 + -3.5 = 3.446221995
x = 3.446221995

Simplifying
x = 3.446221995


Subproblem 2
x + 3.5 = -6.946221995

Simplifying
x + 3.5 = -6.946221995

Reorder the terms:
3.5 + x = -6.946221995

Solving
3.5 + x = -6.946221995

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -6.946221995 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.946221995 + -3.5
x = -6.946221995 + -3.5

Combine like terms: -6.946221995 + -3.5 = -10.446221995
x = -10.446221995

Simplifying
x = -10.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.446221995, -10.446221995}
Solution
x = {3.446221995, -10.446221995}

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